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24 Apr 2025, 08:20
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Of the retailers surveyed, 65 percent owned an online store, and 75 percent owned a physical store. What percent of the retailers owned a physical store but did not own an online store?
(1) 15 percent of the retailers owned an online store but not a physical store.
(2) The number of the retailers who owned both an online and a physical store was five times the number of the retailers who did not own either an online or a physical store.
(1) 15 percent of the retailers owned an online store but not a physical store.
(2) The number of the retailers who owned both an online and a physical store was five times the number of the retailers who did not own either an online or a physical store.
24 Apr 2025, 08:20
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Official Solution:
Of the retailers surveyed, 65 percent owned an online store, and 75 percent owned a physical store. What percent of the retailers owned a physical store but did not own an online store?
From the question:
• {Online} = 65.
• {Physical} = 75.
We want: physical store but not online store, so {Physical only}.
(1) 15 percent of the retailers owned an online store but not a physical store.
{Online only} = 15.
Since {Online} = 65, then {Both} = 65 - 15 = 50.
Since {Physical} = 75, then {Physical only} = {Physical} - {Both} = 75 - 50 = 25.
Sufficient.
(2) The number of the retailers who owned both an online and a physical store was five times the number of the retailers who did not own either an online or a physical store.
This implies: {Both} = 5 * {Neither}.
{Total} = {Online} + {Physical} - {Both} + {Neither}
100 = 65 + 75 - 5 * {Neither} + {Neither}
{Neither} = 10, and thus {Both} = 5 * {Neither} = 50.
Since {Physical} = 75, then {Physical only} = {Physical} - {Both} = 75 - 50 = 25.
Sufficient.
Answer: D
Of the retailers surveyed, 65 percent owned an online store, and 75 percent owned a physical store. What percent of the retailers owned a physical store but did not own an online store?
From the question:
• {Online} = 65.
• {Physical} = 75.
We want: physical store but not online store, so {Physical only}.
(1) 15 percent of the retailers owned an online store but not a physical store.
{Online only} = 15.
Since {Online} = 65, then {Both} = 65 - 15 = 50.
Since {Physical} = 75, then {Physical only} = {Physical} - {Both} = 75 - 50 = 25.
Sufficient.
(2) The number of the retailers who owned both an online and a physical store was five times the number of the retailers who did not own either an online or a physical store.
This implies: {Both} = 5 * {Neither}.
{Total} = {Online} + {Physical} - {Both} + {Neither}
100 = 65 + 75 - 5 * {Neither} + {Neither}
{Neither} = 10, and thus {Both} = 5 * {Neither} = 50.
Since {Physical} = 75, then {Physical only} = {Physical} - {Both} = 75 - 50 = 25.
Sufficient.
Answer: D
01 Nov 2025, 03:32
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I don’t quite agree with the solution. Statement 2 says: The number of the retailers who owned both an online and a physical store was five times the number of the retailers who did not own either an online or a physical store.
I thought either an online or a physical store would mean did not own online but physical or not physical but online. How would I assume that it owned neither from this statement? Not clear.
I thought either an online or a physical store would mean did not own online but physical or not physical but online. How would I assume that it owned neither from this statement? Not clear.
